We present a security analysis of the complete TLS protocol in the Universal Composable security framework. This analysis evaluates the composition of key exchange functionalities realized by the TLS handshake with the message transmission of the TLS record layer to emulate secure communication sessions and is based on the adaption of the secure channel model from Canetti and Krawczyk to the setting where peer identities are not necessarily known prior the protocol invocation and may remain undisclosed. Our analysis shows that TLS, including the Diffie-Hellman and key transport suites in the uni-directional and bi-directional models of authentication, securely emulates secure communication sessions.